THE SMITHSONIAN INSTITUTION. 385 



centimetres (2,500 square millimetres) and are 1 centimetre (0.01 

 metre) apart, is filled with dilute sul])huric acid of the specific gravity 

 1.4 ; then the resistance of the liquid column in the voltameter is — 



1023400 Ml|,g^^5 = 32; 



hence the strength of the current is t > ■ 9 — j denoting hy E the 



electro-motive force, and by K the entire resistance of the j)ile, and 

 assuming for the polarization the approximate value 1,000. 



When a voltameter is inserted in the closing arc of a battery, the 

 principle is no longer true, that a maximum strength of current is 

 obtained when the given number of cups are so arranged that the 

 resistance of the battery is equal to the resistance of the closing arc ; 

 because the supposition on which the demonstration was based, 

 namely^ that in different combinations of the same number of cups 

 the resistances vary in proportion to the square of the electro-motive 

 force, does not hold good here by reason of the polarization in the 

 voltameter. Tlie maximum effect is in favor of those combinations in 

 which more cups stand in a row and fewer beside each other. 



That a change of the maximum should take place in this way, may 

 be easily seen from a special example. In the various combinations 

 of 24 cups, of Daniell's elements, (where E = 470, R = 22,) a wire 

 was inserted, whose resistance was equal to 32 ; the following /orces 

 of current were obtained for these combinations : 



24 X 470 11280 



24 X 22 -{- 32 560 



=z 20. 



2 12 X 470 _ 5640 _ 3^ 

 6 X 22 + 32 164 



3 8 X 470 _ ^m _ 4^ 

 2.7 X 22 -h 32 91 



4 6 X 470 _ 2820 _ ^3 

 1.5 X 22 +32 65 



4 X 470 _ 1880 



0.7 X 22 + 32 47 



40. 



6 3X470 1410 ^ 34 



0.4 X 22 -f 32 41 



Hence, we have the maximum, 43, for the case where the resistance 

 of the battery, 1.5 X 22 =r 33, is nearly equal to that of the closing 

 arc. But, by inserting the above-mentioned voltameter, whose resist- 

 ance is 32, instead of the metallic wire of the same resistance, the 

 strength of current must be less, because the numerator of the above 

 fraction has to be reduced by 1 ,000 ; hence we get the following 

 strengths of currents for the different combinations : 

 25 



